# Archive | Notes

## Advanced Questions Involving Differences of Squares

Suppose we want to find all the integers satisfying is a difference of squares and factorises asand 7 factorises asorsoorororWe may equate factors on either side to give either andorand The first of these gives the simultaneous equations The solution isand The second of these gives the simultaneous equation The solution is The first of […]

## The Distance Between Two Points

Suppose we want to find the length of the line between A and B in the diagram below. We draw a straight line between A and B, and make this rhe hypotenuse of a right angled triangle by drawing a horizontal line from A to a point directly below B and another line down from […]

## Scale Factors and Negative Enlargements

A ‘normal’ enlargement casts a ‘shadow’ of the shape, which may be larger or smaller than that shape to be enlarged. The scale factor k is positive, with the enlarged shape being k times as far from the centre of enlargement as the original shape. If the scale factor is more than one, the enlarged […]

## BODMAS

BODMAS stand for B – Brackets O – Powers D – Division M – Multiplication A – Addition S – Subtraction we carry out these operations in the order brackets, order (roots and powers), division, multiplications, addition, subtraction. Example: calculate We carry out the multiplication first: Example: Calculate We carry out the operation inside the […]

## Dividing in Certain Ratios

Three men – Alf, Bob and Cliff – have £150 to share between them for a job of work. Being all fair of mind they decide to divide the money in proportion to the work they have done. They decide therefore to share the money in the ratio 4:5:6. They draw up the following table. […]

## Stem and Leaf Diagrams

A stem and leaf diagram is a compact way to display a list is a way that enables the shape of the list to be quickly perceived. For example we start with a list of numbers that represent the heights of 50 adults men: 190, 149, 150, 172, 183, 190, 178, 189, 179, 176, 164, […]

## Cumulative Frequency Curves, Quartiles, Interquartile Range and Median

Cumulative frequency curve enable you to read off the number of values that are less than a certain value, more than a certain value or between two values. We may also read off the lower and upper quartiles and the median, and find the inter – quartile range. We start wit a raw frequency table. […]

## Factorising General Quadratics and Differences of Squares

Any expression of the formcannot be factorised as with simple quadratics, by finding factors of c. Instead there is a slightly more complicated procedure, best illustrated by an example: Factorise Take out any common factor. Every term in the above expression has a factor 3, so we may write the expression as Multiply the coefficient […]

## The Relationship Between Boxplots and Cumulative Frequency Curves

The relationship best illustrated by using the same x axis for boxplot and curve. Minimum, lower quartile, median, upper quartiles and maximum clearly correspond.

## Multiplying Decimal Numbers

If you can multiply numbers you can multiply decimals. It is only a matter of, once you have multiplied two numbers, of counting the number of decimal places. Example: 0.3*0.2 3*2=6 0.1 has one number after the decimal point and 0.2 has one number after the decimal point so there are two numbers after the […]